Exploring Standard Form: Jellyfish

Consider the following situation.

Mako and Hammie are ordering food for a huge party. They have been arguing back and forth on how many jellyfish sandwiches and how many tunafish sandwiches they should order. Each jellyfish sandwich will cost 6 sand dollars and each tunafish sandwich will cost 3 sand dollars.

  1. Let J = the # of jellyfish sandwiches they order
    Let T = the # of tunafish sandwiches they order
    How do the variables relate? That is, what do you think about dependent and independent variables for this situation? Explain.
  1. Each of these equations has meaning in the context of the problem. Explain what each one means.
    (Hint: If you need, simply replace the variables for the words we used above to define them and the math symbols for how we say them.)
  1. Suppose that Hammie wants to order a total of 100 sandwiches. List 5 different ways he could order some tunafish and some jellyfish sandwiches such that the total is 100.

  1. Using the graph, plot the points that would represent the 5 different ways you described that he could order a total of 100 sandwiches.
    (Since neither J nor T is a true independent variable, let’s arbitrarily choose J to go on the horizontal axis.)
  1. The points from the last problem should have formed a straight line.
  2. Use a straight edge to draw in the line through the points.
  3. Extend that line so it reaches both axes and label it “100 total sandwiches.”
  4. Where does that line intersect each axis? What do these intersection points mean in the context of the situation?
  1. Mako thinks they should order only 80 total sandwiches. Graph the line “80 total sandwiches” using the previous graph. Explain how you determined where the line would go.
  1. Where do you think the line “60 total sandwiches” would be on the graph? How would it compare to the “80 total sandwiches” and “100 total sandwiches” lines?

  1. Reread to find out how much each sandwich will cost Mako and Hammie. Then complete the following tables.

# of jellyfish sandwiches / 1 / 8 / 25 / 50 / 63 / 99 / … / J
Cost ($)
# of tunafish sandwiches / 1 / 5 / 10 / 35 / 72 / 100 / … / T
Cost ($)
  1. How much would it cost Mako and Hammie to order 40 tunafish and 60 jellyfish sandwiches?

How much would it cost Mako and Hammie to order 60 tunafish and 40 jellyfish sandwiches?


Mark those costs you just found on the following graph by plotting the correct point and labeling it with the cost. For example, the point (0, 0) would be labeled “$0” since it would cost $0 to order 0 jellyfish and 0 tunafish sandwiches.

Continue to plot points and label the cost that each of those points represents for each of the “nice” intersections of the grid—like (0, 20), (40, 0), (20, 40), etc.

Explain what patterns you see in the costs as you move throughout the graph.

  1. Let C = the total cost in sand dollars for their order. Write an equation that describes the total cost, C, for Mako and Hammie to order T tunafish and J jellyfish sandwiches.
  1. Each of these equations also has meaning in the context of the problem. Explain what each one means.
  1. Mako and Hammie finally decided they need to order at least 60 total sandwiches. Write an equation that models ordering exactly 60 sandwiches. Then graph the model. (Be sure to label your linear model in the graph.)

They also decided they cannot spend more than 480 sand dollars. Write an equation to model spending exactly 480 sand dollars. Then graph this model. (Be sure to label the linear model.)

Shade in the region of the graph that would meet all the conditions “at least 60 total sandwiches” and “cannot spend more than 480 sand dollars”. Explain how you determined which area of the graph to shade.

  1. Mako and Hammie’s friend G.W. noted that they should have at least 40 jellyfish sandwiches even though they are more expensive. Write an inequality that models this. Explain how you would graph this inequality.
  1. Provide three different ways that Mako and Hammie could order sandwiches such that they order at least 60 total sandwiches, they do not spend more than 480 sand dollars and, they have at least 40 jellyfish sandwiches.